When opening a chat window, the history (previously exchanged messages) for that contact are shown.
In that part (the history), the nickname of all participants should be used. However, since 2.9.0, the messages that you sent yourself that are displayed in that history are prepended with your JID, instead of your nickname.
This is easily reproducible: open a chat, type a message, close the chat window, and open it again. You should see the message prefixed with your nickname, not with your JID.